It is known to provide cancellation/demodulation systems that include successive interference cancellation (SIC) receivers and satellite systems that employ channel reuse in the satellite downlink. In multiuser applications, for example, a SIC receiver can be used to cancel nonlinear-distorted interference, that is associated with a previously-demodulated stronger user, in order to demodulate the next weaker user.
In a satellite-transponder communication system a local terminal communicates with a remote terminal over a duplex satellite communications link in which a loop-back transponder sends a transmitted signal to both the terminal receivers. The transponder is designated loop-back, or alternatively “bent-pipe”, as its operation is limited to bandpass filtering, frequency translation and amplification and does not include demodulation and remodulation. Thus, the downlink to the local terminal contains a relayed-interference signal corresponding to the transmitted signal designated for the remote terminal. Conventionally, to avoid this relayed interference, a satellite communication link can only transmit or receive signals in one direction for a single access use. For example, in a frequency-division multiple access system, a separate bandwidth allocation for the local terminal and a separate bandwidth allocation for a remote terminal would be necessary for communication in both directions. However, the relayed-interference signal at the local transmitter terminal could be generated at the same terminal receiver to cancel this relayed interference. Such cancellation provides reuse of the frequencies in the local terminal bandwidth allocation for return link communication between the remote terminal and the local terminal. However, the power amplifier in the local transmitter is not perfectly linear and may limit the amount of cancellation of the relayed interference and preclude frequency reuse of the downlink channel. The power amplifier can be characterized by a zero-memory nonlinearity. The transmit/receive channel includes linear filtering both before and after the nonlinearity, resulting in a dispersive nonlinear channel. The dispersive nonlinear distortions in such a channel cannot be eliminated by either linear filtering or zero-memory nonlinear compensation at the receiver. Thus, any nonlinear compensation to increase the cancellation level will require techniques that can cope with dispersive nonlinear distortions.
Antenna sizes at the respective terminals, fade margin considerations, and modulation choices affect the level of achievable cancellation in these satellite systems. When the local terminal has a larger diameter antenna, with gain GH, than the remote terminal with an antenna of gain GR, the interference problem will generally be more difficult at the larger antenna terminal. For both signal directions the received bit energy is proportional to the antenna gain product GHGR and the transmitted energy per bit. In data transmission with a fixed modulation type the bit error probability is proportional to the received bit energy. Since the antenna gain product is the same in both directions, the transmitted energy per bit can be about the same for the local-to-remote direction as for the remote-to-local direction. However, because the transponder relays the transmitted signal back to the same terminal, the relayed interference signal has received bit energy proportional to the local terminal antenna gain squared. Additionally, although the terminals share the same physical path resulting in the same fade statistics for each direction, differences in the terminal fading compensation systems can result in different power outputs and a more difficult interference problem for the terminal with the higher power. Finally, the data rate and/or the modulation types may be different requiring one of the terminals to transmit more power and thus increasing the interference problem at the associated receiver terminal. These asymmetrical factors in satellite-transponder applications can lead to relayed interference in a frequency-reuse application at the local terminal that is as much as 10 dB stronger than the desired signal from the remote terminal. In satellite systems, bit-error rate performance goals are typically within 0.3 to 0.5 dB of theoretical limits. The cancelled relayed-interference signal is approximately complex Gaussian distributed so that its power adds to the channel noise at the receiver. If 0.4 dB is allocated for performance degradation due to a residual relayed-interference signal alone, the cancellation must push the relayed-interference signal approximately 10 dB below the noise. For the additional 10 dB of interference discussed above relative to the desired remote terminal signal and a signal-to-noise ratio of 7 dB for the desired remote terminal signal, the required cancellation would be equal to 10+10+7=27 dB. Accordingly, compensation of dispersive nonlinear distortions are required if these distortions are greater than this −27 dB threshold.
Existing systems have been developed to provide multiple-access reuse in full-duplex satellite communication systems that operate with a loop-back transponder. These systems use either discrete-time information signals prior to modulation or continuous-time modulation signals prior to the power amplifier to produce a reference signal for purposes of cancellation of the relayed interference at the receiver. U.S. Pat. No. 5,596,439 ('439), describes an open-loop technique consisting of measurement techniques followed by interference reduction based on measured link parameters that are applied to the reference signal. The technique described is for applications where “the relay channel is assumed to be linear” so that the receiver composite signal contains “a copy of said source signal”. In nonlinear systems the signal to be cancelled is distorted such that the receiver composite signal does not contain a copy. The estimating means in the '439 patent is realized in Parameter Estimator 28 that measures the linear parameters of delay, frequency, phase, and gain. These parameters do not include nonlinear distortions effects so cancellation levels are limited. Further, errors in open-loop parameter measurement such as Parameter Estimator 28 can significantly degrade subsequent interference reduction relative to a canceller operating in an adaptive closed-loop system.
U.S. Pat. No. 6,859,641 B2 and U.S. Pat. No. 7,228,104 B2 ('641/'104) each describe an adaptive cancellation system that converts a sample of the IF transmitted signal to digital form and converts the IF received signal containing the relayed interference to digital form. Frequency, phase, gain, and delay parameters of the sample of the transmitted signal are adjusted to produce a compensating signal that is added to the digital form received signal to produce a signal of interest. The signal of interest can be converted back to an intermediate frequency for interface with a down-stream demodulator. The 641'/'104 technique does not address distortions due to nonlinearities in the local terminal power amplifier. The reference signal used for cancellation has not passed through the power amplifier nonlinearities and the resulting nonlinear distortions cannot be removed.
In these prior art systems it may be necessary to significantly reduce the power amplifier operating level to insure that the nonlinear distortions are small enough to allow for channel reuse. Such “backoff” of the power amplifier is undesirable because of loss of fade margin.
U.S. Pat. No. 7,522,877 B1 describes an interference-reduction system for the local terminal in the satellite communication configuration described above. The interference-reduction system digitizes and converts to baseband the local terminal IF transmit signal and transfers the bits in the baseband digital signal to a buffer in the local receiver to produce a replica of the local transmitted signal. The replica is then scaled, delayed and distorted to reduce the transponder-relayed local interference signal in a received signal that also contains multiple remote terminal signals. Since the interference reduction is over the local signal bandwidth rather than a single remote terminal signal subband, the effects of nonlinearities in the local transmitter can critically limit interference reduction. Accordingly, the 877 patent describes the generation of AM-Normgain and AM-PM correction arrays that are used for the distortion modification of the local transmitted signal replica.
According to the above described techniques, optimum receiver filtering and subsequent demodulation of the remote-terminal signal is not disclosed and the interference cancellation is over the signal bandwidth of the local terminal signal. The optimum receiver filter for the remote terminal signal is the matched filter fd*(−t) corresponding to the remote-terminal transmit filter with impulse response fd(t). In digital data systems, it is desirable to perform cancellation upon discrete-time signals after optimum receiver filtering and sampling rather than upon the associated continuous-time signal prior to receiver filtering and discrete-time sampling. This follows, first, because the discrete-time signal bandwidth is equal to the digital-modulation signal rate which is smaller than the continuous-time signal bandwidth. In general, interference cancellation levels are greater in a smaller bandwidth. Second, the optimum filtering minimizes the additive channel noise that can degrade cancellation performance.
Distortions produced by a signal that traverses a nonlinear channel are often characterized by a Volterra series expansion. The Volterra series is a generalization of the classical Taylor series. See “Nonlinear System Modeling Based on the Wiener Theory”, Proceeding of the IEEE, vol. 69, no. 12, pp. 1557-1573, December 1981. U.S. Pat. No. 3,600,681 describes a nonlinear equalizer based on a Volterra series expansion of nonlinear intersymbol interference (NISI) in a data communication system. In “Adaptive Equalization of Channel Nonlinearities in QAM Data Transmission Systems”, D. D. Falconer, Bell System Technical Journal, vol. 57, No. 7, September 1978, [Falconer], the Volterra series for NISI is used in a passband decision feedback equalizer. This equalizer is adapted by adjusting the coefficients of the Volterra series expansion by a gradient algorithm. In Falconer, it was concluded that “the number of nonlinear terms . . . is potentially enormous” and that “the simulation results indicated that inclusion of a large number of nonlinear terms, . . . may be necessary.” The complexity of the Volterra series expansion for either voiceband telephone channels or satellite channels with nonlinear power amplifiers has been recognized in “Efficient Equalization of Nonlinear Communication Channels, W. Frank and U. Appel, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. III, Apr. 21-24, 1997. [Frank]. In Frank, it is described that a decision feedback equalizer (DFE) uses a nonlinear structure that is a good approximation to the general Volterra filter but with reduced complexity. The nonlinear structure is based on an equivalent lowpass model of a 3rd order bandpass nonlinearity. Because this Volterra series approximation provided better improvements at higher signal-to-noise ratio, it is concluded in Frank that the Volterra approximation DFE is better suited to the voiceband telephone channel than radio communications.
Rather than provide compensation for nonlinear distortions at the receiver by using nonlinear equalizers, there are predistortion techniques that can be applied in the transmitter before the nonlinear channel. In “A Data Predistortion Technique with Memory for QAM Radio Systems”, IEEE Trans. Communications, Vol. 39, No. 2, February 1991, G. Karam and H. Sari, [Karam], explicit expressions are derived for the 3rd and 5th order inverse Volterra kernels. Karam also notes that the finite-order inverses grow “very rapidly” with the Volterra order p and the discrete-time signal memory span K. These small order/memory span Volterra inverses are compared in Karam with a lookup memory encoder (referred to as “global compensation” in Karam) that predistorts each possible discrete-time signal data value such that at the discrete-time channel output the center of gravity of the received points is in the correct position in the discrete-time signal constellation. The RAM implementation of the lookup memory encoder requires K log2 M address bits where M is the modulation alphabet size. By using a rotation technique based on the center discrete-time signal in the memory span, the number of address bits can be reduced in M-ary QAM by two because of quadrature symmetry. For a given memory span and a practical number of address bits, it is described in Karam that the lookup memory encoder outperforms the Volterra inverse predistortion. However, Karam does not describe a technique for initializing and adapting the lookup memory encoder in the presence of additive noise. Unfortunately, the preamble length for initialization of a predistortion lookup memory encoder can be excessively large. The preamble length is on the order of AMK-1 discrete-time signals where A is the averaging time to make the additive noise small compared to an acceptable level of residual distortion. A typical averaging time of 100 discrete-time signals for 8PSK with K=5 would require a preamble of over 400,000 discrete-time signals. This difficulty with initialization and adaptation of distortion compensation systems using lookup table techniques is also noted in “Modeling and Identification of a Nonlinear Power-Amplifier with Memory for Nonlinear Digital Adaptive Pre-Distortion”, Proceedings of the SPAWC Workshop, 15-18.6.2003, Rome Italy, by Aschbacher et al, [Aschbacher]. Also recognizing the slow convergence and large number of coefficients in the Volterra series expansion, it is suggested in Aschbacher to identify a nonlinear power amplifier by a simplified Wiener-model consisting of a linear filter followed by a zero-memory nonlinearity. An adaptive Least Means Squares algorithm is used to adapt and track parameters in the linear filter and the zero-memory nonlinearity to minimize the mean square error between the sampled data output of the nonlinear power amplifier and the simplified Wiener-model. This minimization is over the signal bandwidth rather than the smaller discrete-signal bandwidth and the minimization does not include receiver filtering contributions to the nonlinear intersymbol interference. As a result interference cancellation with the Aschbacher identification model would not be as effective as a technique that is receiver based and minimizes a mean square error in the received discrete-time signal values.
Accordingly, there is a need at a receiver terminal in certain digital communication systems for desired-signal demodulation that includes cancellation of nonlinear distorted interference under conditions where an undistorted version of the interference can be produced. Further, it would be desirable to utilize nonlinear techniques that provide faster convergence of the nonlinear series expansion and better performance than prior art systems based on conventional Volterra series expansion techniques. Additionally, it would be desirable that these nonlinear techniques can be initialized and adapted to changing conditions more effectively than prior art lookup memory techniques.